Fluid Mechanics – Laminar Flow in Circular Pipes Definition and Criterion: The internal flow in a circular pipe is called laminar (streamline) when the Reynolds number, Re = (rho * V * D) / mu, is less than 2000. This empirical threshold separates orderly viscous-dominated motion from transitional and turbulent regimes in typical engineering practice.

Introduction:
The question tests the fundamental criterion for classifying internal flow in circular pipes into laminar, transitional, or turbulent regimes using the Reynolds number. Understanding this threshold is essential for selecting formulas for head loss, velocity profiles, and mass/heat transfer correlations.

Given Data / Assumptions:

• Newtonian fluid flowing steadily in a circular pipe.
• Reynolds number Re = (rho * V * D) / mu, where rho is density, V is mean velocity, D is pipe diameter, and mu is dynamic viscosity.
• Conventional engineering threshold values are used.

Concept / Approach:

Reynolds number compares inertia forces to viscous forces. Low Re implies viscous forces dominate, producing orderly layers of fluid (laminar flow). Empirically, for flow in smooth circular pipes, laminar flow persists when Re is below about 2000; between roughly 2000 and 4000 is transitional; above about 4000 is turbulent for most practical conditions.

Step-by-Step Solution:

Verification / Alternative check:

In laminar flow, the theoretical velocity profile is parabolic and head loss is given by the Hagen–Poiseuille relation. These relations agree with experiments only when Re is sufficiently low (well below transitional values), reinforcing the Re < 2000 guideline.

Why Other Options Are Wrong:

False: Contradicts the accepted threshold for circular pipes. Only for inviscid fluids: Inviscid assumption removes viscosity, making Re undefined and the classification meaningless. Only for open channels: Reynolds criteria given here applies to internal pipe flow, not open-channel regimes.

Common Pitfalls:

Confusing exact universal limits with practical thresholds; misusing hydraulic diameter for noncircular ducts; ignoring surface roughness and disturbances that can trigger early transition even below 2000 in extreme cases.

Final Answer:

True